Vectors> The points (0,-1,-1), (-4,4,4),(4,5,1) an...

The points (0,-1,-1), (-4,4,4),(4,5,1) and (3,9,4) are
(A) Collinear
(B) Coplanar
(C) Forming a square
(D) None of these

Satviki Pathak , 10 Years ago

Grade 11

2 Answers

Yash Jain

Last Activity: 10 Years ago

The answer is (B)
Lets check all the options.
for A):- the line through the points (0,-1,-1) and (-4,4,4) is x/-4 = (y+1)/5 = (z+1)/5
The point (4,5,1) does not satisfy this equation, so points are not collinear.
for B):- the equation of plane containing the points (0,-1,-1), (-4,4,4) and (4,5,1) is 5x-7y+11z+4=0 (determinant method). This equation is satisfied by (3,9,4). So the points are coplanar.
Now there is no need to verify C) but still lets see.
for C):- Lets call the given points as A,B,C,D resp. So DRs of AB is Hence the answer is B
). For AB _I_ BC, l1l2 + m1m2 + n1n2 = 0. So (-4).8 + 5.1 + 5.(-1) = 0 which is false. So the given points do not form a square.() and that of BC is (

Yash Jain

Last Activity: 10 Years ago

The answer is (B)
Lets check all the options.
for A):- the line through the points (0,-1,-1) and (-4,4,4) is x/-4 = (y+1)/5 = (z+1)/5
The point (4,5,1) does not satisfy this equation, so points are not collinear.
for B):- the equation of plane containing the points (0,-1,-1), (-4,4,4) and (4,5,1) is 5x-7y+11z+4=0 (determinant method). This equation is satisfied by (3,9,4). So the points are coplanar.
Now there is no need to verify C) but still lets see.
for C):- Lets call the given points as A,B,C,D resp. So DRs of AB is ). For AB _I_ BC, l1l2 + m1m2 + n1n2 = 0. So (-4).8 + 5.1 + 5.(-3) = 0 which is false. So the given points do not form a square. Hence the answer is (B)(say) and that of BC is (say